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5713 Shi ’s National Road System

During the of ancient (476 BC to 221 BC), there were seven kingdoms in China — they were , , , , , and Qin. was the king of the Qin. Through 9 years of wars, he finally conquered all six other kingdoms and became the first of a unified China in 221 BC. That was — the first imperial dynasty of China(not tobe confused with the Qing Dynasty, the last dynasty of China). So Ying Zheng named himself ”Qin Shi Huang” because ”Shi Huang” means ” ” in Chinese. Qin Shi Huang undertook gigantic projects, including the first version of the , the now famous city-sized mausoleum guarded by a life-sized Terracotta , and a mas- sive national road system. There is a story about the road system: There were n cities in China and Qin Shi Huang wanted them all be connected by n−1 roads, in order that he could go to every city from the capital city . Although Qin Shi Huang was a tyrant, he wanted the total length of all roads to be minimum,so that the road system may not cost too many people’s life. A daoshi (some kind of monk) named Fu told Qin Shi Huang that he could build a road by magic and that magic road would cost no money and no labor. But could only build ONE magic road for Qin Shi Huang. So Qin Shi Huang had to decide where to build the magic road. Qin Shi Huang wanted the total length of all none magic roads to be as small as possible, but Xu Fu wanted the magic road to benefit as many people as possible — So Qin Shi Huang decided that the value of A/B (the ratio of A to B) must be the maximum, which A is the total population of the two cites connected by the magic road, and B is the total length of none magic roads. Would you help Qin Shi Huang? A city can be considered as a point, and a road can be considered as a line segment connecting two points.

Input

The first line contains an integer t meaning that there are t test cases (t ≤ 10). For each test case: The first line is an integer n meaning that there are n cities (2 < n ≤ 1000). Then n lines follow. Each line contains three integers X, Y and P (0 ≤ X,Y ≤ 1000, 0 < P < 100000). (X,Y ) is the coordinate of a city and P is the population of that city. It is guaranteed that each city has a distinct location.

Output

For each test case, print a line indicating the above mentioned maximum ratio A/B. The result should be rounded to 2 digits after decimal point. ACM-ICPC Live Archive: 5713 – Qin Shi Huang’s National Road System 2/2

Sample Input 2 4 1 1 20 1 2 30 200 2 80 200 1 100 3 1 1 20 1 2 30 2 2 40

Sample Output 65.00 70.00